Microscopic Approaches To Traffic Modeling
There are two basic approaches to traffic modeling namely: The macroscopic approach and the microscopic approach. In the macroscopic approach, traffic is viewed as fluid flow or heat transfer phenomena. As a result, vehicles (cars) are not modeled individually but as a group of entities moving on a system. The microscopic approach looks at individual driving behaviours. Here we are interested in the microscopic approach.
The car following model is a microscopic approach to traffic modeling and it started with the work of Herman and Gazis. Here cars are modeled individually. Also car and human interactions are modeled explicitly and a driver follows another car by considering; the distance, speed difference, reaction time and vehicle performance.
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In particular for m = l = 0 one obtains the original model (GM model) and for m = 0, l = 1 one obtains the first modification and so …show more content…
This model assumes that each car tries to attain an optimal velocity that is dependent on its spacing with the preceding one. In particular, it states that the acceleration of the following car is directly proportional to the optimal velocity function minus its own (instant) velocity (that is the difference between the optimal velocity function and the velocity of the following car), where the constant of proportionality is the constant sensitivity coefficient. The optimal velocity model does not take into account the response/delay time. This can be achieved by modifying the model so that the acceleration of the following car adjusted to some time lag is directly proportional to the optimal velocity function minus its own (instant) velocity where the constant of proportionality is the gain constant of the response process. Unlike the GM model the optimal velocity model allows the possibility of different kind of cars with different speed ranges. The optimal velocity model can be generalized and to do this one assumes that the optimal velocity function depends not only on the headway of each car but also on the headway of the immediate preceding
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